1. Field of the Invention
This invention relates to precision tracking of targets (aeroplanes, missiles, launch vehicles, launchsites, landmarks, etc.) with a spacecraft, and more particularly to the use of integral pulse frequency modulation (IPFM) reaction jets for tracking the target with small tracking errors. Additionally, this invention is related to stabilizing the interaction of control jets with flexible portions of the spacecraft and to suppressing vibration to minimize jitter.
2. Description of the Related Art
Farrenkopf et al. (see Farrenkopf, R. L., Sabroff, A. E., and Wheeler, P. C., "Integral Pulse Frequency On-Off Control," Guidance and Control II, Edited by R. C. Langford and C. J. Mundo, Vol. 13, Progress in Astronautics and Aeronautics, Academic Press, New York, 1964, pp. 185-216) presented a complete procedure for designing a single-axis IPFM controller, and compared its performance with a saturating proportional-plus-derivative controller and a relay controller with a deadband and hysteresis. Abdel-Rahman (see Abdel-Rahman, T.M.M., The Effects of Structural Flexibility on the Nonlinear Attitude Control of Spacecraft, Institute for Aerospace Studies, University of Toronto, UTIAS Report No. 222, December 1977) compared it further with a dual time constant pseudorate controller. The unique characteristics and benefits of an IPFM controller are: It activates a thruster pulse of constant width whenever the integral of a linear combination of position and rate errors exceeds a certain threshold; the frequency of the jet firing is thereby modulated, keeping the pulsewidth constant. Farrenkopf, et al. (see Farrenkopf, Sabroff, and Wheeler, above) conclude that because of integration of the errors, the effect of sensor noise is considerably mitigated and the attitude control is much smoother than that by a pseudorate controller. This is true also because of availability of the rate error. Owing to these features, the IPFM controller is not as debilitated by structural flexibility as a pseudorate controller is, even when the natural damping of the structure is low (.zeta..apprxeq.0.0025) and the sensor time lag large (see Abdel-Rahman, above). As will be disclosed below, IPFM controllers are therefore utilized herein for target tracking, requiring large angle multi-axis attitude motions, and for spacecraft attitude control under disturbance torques.
Thrusters are particularly prone to exciting flexible modes of a spacecraft. Therefore, it is imperative to examine if flexibility degrades the controller performance, induces instability, or under some favorable circumstances the controller suppresses the vibrations. The interaction between nonlinear reaction jet controllers and structures has been analyzed in the past using describing function and Liapunov techniques. These analyses tend to be rather sophisticated, however. Moreover, symmetric elastic modes usually do not interact with spacecraft attitude, but when they do, owing to their moment arm from the vehicle mass center, thrusters must be located carefully because their translational force is not of the same genre as the angle measured by an IMU gyro. Gevarter (see Gevarter, W. B., "Basic Relations for Control of Flexible Vehicles," AIAA Journal, Vol. 8, No. 4, 1970, pp. 666-672) furnished corresponding linear stability conditions.